From the book!
Suppose there are two players A and B playing a game.
The game begins with number 0 and in one turn a player can add to the current number any natural number from 1 through 9. The player who reaches the number 100 first wins.
The first move is made by A.
Who will win?
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1 solution
Whatever number A starts with (f. ex 4) B will just have to add a number so the result will be 10. In this case, B adds 10-4=6. Thus, each turn B ends, the result will a multiple of ten. As 100 is a multiple of ten, B will win every time if he plays optimally.